We have measured the dielectric constant, ε{lunate}, in the semiconductors La2CuO4+x and EuBa2Cu3O6+x. In both cases the crystals are grown by standard techniques and annealed in inert gases, which leads to a semiconductor with x{all equal to}0, whereas an oxygen anneal produces a superconductor. We have shown earlier that these results are intrinsic to La2CuO4 by measuring the temperature dependence of ε{lunate} at high frequencies. The intrinsic values are ε{lunate} = 23 for the c-axis of both materials, ε{lunate} = 45 in the a-b plane of La2CuO4, and ε{lunate} = 32 in the a-b plane of EuBa2Cu3O6. The implications of these large dielectric constants for high temperature superconductivity are discussed. © 1990.